3) Which of the following equation represents the temperature distribution (T (R, t)) for the instantaneous point heat source by considering the infinite body and zero initial temperature? (Where: R = x2 + y2 + z2 a is the thermal diffusivity, p is the density, Cp is the specific heat and Q is the heat input) Q а. PC,(4rat)/2) Cæp (-R²/4qt) b. PC,(4rat)") -еap (- R?/4ot) Q с. pC,(4mat)W/2) Cap (-a²/4at) егp (— R*/4at) PC,(47)(3/2) d.
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- In the United States, energy for household heating is generally sold using English units, e.g., therm, gal, and cord. A house in Wisconsin uses 1200 therms of thermal energy during the heating season. Calculate the cost of fuel if the furnace uses (a) natural gas with an efficiency of 70%; (b) No. 2 fuel oil, efficiency 65%; (c) kerosene, efficiency 99.9% (unvented); and (d) wood with l5% moisture with an efficiency of 50%. Use the data in Tables 2.2, 2.7, and 2.13. The efficiencies are based on the HHV. Assume the cost of natural gas is $8/MBtu, the cost of No. 2 fuel oil is $3/gal, the cost of kerosene is $3.50/gal, and the cost of wood is $100/cord. Assume the bulk density of cord wood is 30 lbm/ft3 .1. A LEV system has a centrifugal fan rotating at 714 rpm. The airflow is 6210 cfm, the fan total pressure is 4.07” w.g., and the brake horsepower is 3.12 hp. If the rotating speed is decreased to 620 rpm, what are the brake horsepower? a. 1.43 hp b. 2.04 hp c. 2.41 hp d. 2.67 hp 2.A LEV system has a centrifugal fan rotating at 714 rpm. The airflow is 6210 cfm, the fan total pressure is 4.07” w.g., and the brake horsepower is 3.12 hp. If the rotating speed is decreased to 620 rpm, what are the new value for fan total pressure? 4.15" w.g. 3.87" w.g. 3.07" w.g. 3.94" w.g.HANDWRITTEN AND FINAL ANSWER MUST BE IN ENGLISH UNITS. Show solution. An experimental gas turbine engine is under development to increase its mechanical efficiency. It has a turbine efficiency of 95% and compressor efficiency of 85%. The following parameters are provided: P1 = 550 kPa, T1 = 25 deg C, rp = 5.5, T3 = 1450 deg C, Wnet = 5500 kW. Compute for the (a) flow rate and (b) mean effective pressure. Consider Ethane as your working fluid.
- The temperatures of the 20 ºC 25 ºC 30 ºC water at outlet Task 1 Explain the system parameters using the Non- Flow Energy EquationA chemicals company wants to optimize the power consumption of their air compressors. Their Design Engineers proposed to replace their Single-stage Adiabatic Compressors with the following: a. Isothermal Compressorb. Two-stage Compressor with intercoolingc. Four-stage Compressor with intercooling In order to justify the replacement, the percentage of the energy per mass (J/g) saved by each proposed compressor system should be calculated. Savings should be at least 40%. Determine which of the three proposed compressors will meet the criterion. The flow rate of air required is 600 ft3/min at 70 °F and 14.7 psi, which should be compressed to a final pressure of 2,000 psig. The relative molecular mass of the gas is 28, isentropic constant is 1.40, and density of air is 1.204 kg/m3.1) Describe how actual internal combustion engine cycle (i.e. Otto and Diesel) thermal efficiency differ from the ideal one at the same power output. 2) Discuss the dependency of the thermal efficiency of the ideal Otto cycle oncompression ratio and engine knock. 3a) Discuss, in your own words, the concepts of velocity boundary layer and temperature boundary layer. Provide some analysis of how and why these two concepts are important in convective heat transfer 3b) For a flat plate, discuss in your own words, how the rate of heat transfer and convective heat transfer coefficient are determined for forced convection and natural (free) convection. In your discussion, analyse how laminar and turbulent flows are treated. 4. A 9 kN tensile load will be applied to a 50 m length of steel wire with E=200 GPa. Knowing that the normal stress must not exceed 150 MPa and that the increase in the length of the wire should be at most 25 mm, determine the smallest diameter wire which can be used.
- Project 2You are an engineer working in a company that provide compressors for food industry, your mangerasked you to do research to investigate the different compressor types along with their applications A. Discuss the possible faults and potential hazards associated with compressor usage.B. Derive the volumetric efficiency formula for an ideal reciprocating compressor volume ratio.C. Discuss the parameters that affect the volumetric efficiency of a reciprocating compressor.1. For a given pump, the diameter, the gauge pressures at the inlet and outlet are −30 × 103 P a and 200 × 103 P a, respectively. If the flow rate is 0.1 m3/s, and the power required is 25 kW, find the efficiency. The intake and discharge are at the same height. 2. The impeller of a radial-flow turbine has an outer radius of 4 f t, turning at 200 rpm. The volume flow rate is 1000 ft3/s, and it discharges in the axial direction. Neglect all losses. If the tangential component of the velocity at the inlet is 5 f t/s, find: (a) The torque exerted on the impeller. (b) The power developed by the machine.In an absorption refrigerator, the energy driving the process is sllPplied not as work, but as heat from a gas flame. (Such refrigerators commonly use propane as fuel, and are used in locations where electricity is unavailable. *) Let us define the following symbols, all taken to be positive by definition: Qf = heat input from flame Qe = heat extracted from inside refrigerator Qr = waste heat expelled to room Tf = temperature of flame Te temperature inside refrigerator Tr = room temperature Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Tf, Te, and Tr alone.
- The effort to build an engine which is 100% efficient is:Will be achieved some dayNot PossiblePossibleIs slightly delayed3. Assume the turbine as an incompressible flow machine. The average meridional speed is given as 150m/s. The flow coefficient is 0.5. Determine the blade speed that satisfies the above conditions.4. In a two-dimensional compressor cascade, inlet stagnation air pressure is 1.5 bar and inlet stagnation temperature is 330K. For an inlet Mach number of 0.75 and an inlet flow angle of 500, the exit flow angle is measured as 15.80. Determine the mass flow rate per unit frontal area, the exit Mach number and the static pressure ratio across the cascade. Assume the flow is isentropic.An air conditioning unit works by taking heat out of a room. As the refrigerant gas expands in the cooling coils, it absorbs heat from the circulating air in the room. This heat is then released as the refrigerant is compressed by the part of the unit that is directed out of the room. The unit serves like a heat pump for the room. Since a refrigerator works in a similar manner, can t also be used to maintain a cool temperature inside a room? Justify your answer.